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Dynamics of a vortex ring in a rotating fluid
- R. Verzicco, P. Orlandi, A. H. M. Eisenga, G. J. F. Van Heijst, G. F. Carnevale
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- Journal:
- Journal of Fluid Mechanics / Volume 317 / 25 June 1996
- Published online by Cambridge University Press:
- 26 April 2006, pp. 215-239
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The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier–Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a ‘degree of polarization’.
If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown.
Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.
Dynamics of a vortex ring moving perpendicularly to the axis of a rotating fluid
- A. H. M. EISENGA, R. VERZICCO, G. J. F. VAN HEIJST
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- Journal:
- Journal of Fluid Mechanics / Volume 354 / 10 January 1998
- Published online by Cambridge University Press:
- 10 January 1998, pp. 69-100
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The dynamics of a vortex ring moving orthogonally to the rotation vector of a uniformly rotating fluid is analysed by laboratory experiments and numerical simulations. In the rotating system the vortex ring describes a curved trajectory, turning in the opposite sense to the system's anti-clockwise rotation. This behaviour has been explained by using the analogy with the motion of a sphere in a rotating fluid for which Proudman (1916) computed the forces acting on the body surface. Measurements have revealed that the angular velocity of the vortex ring in its curved trajectory is opposite to the background rotation rate, so that the vortex has a fixed orientation in an inertial frame of reference and that the curvature increases proportionally to the rotation rate.
The dynamics of the vorticity of the vortex ring is affected by the background rotation in such a way that the part of the vortex core in clockwise rotation shrinks while the anti-clockwise-rotating core part widens. By this opposite forcing on either side of the vortex core Kelvin waves are excited, travelling along the toroidal axis of the vortex ring, with a net mass flow which is responsible for the accumulation of passive scalars on the anti-clockwise-rotating core part. In addition, the curved motion of the vortex ring modifies its self-induced strain field, resulting in stripping of vorticity filaments at the front of the vortex ring from the anti-clockwise-rotating core part and at the rear from the core part in clockwise rotation. Vortex lines, being deflected by the main vortex ring due to induction of relative vorticity, are stretched by the local straining field and form a horizontally extending vortex pair behind the vortex ring. This vortex pair propagates by its self-induced motion towards the clockwise-rotating side of the vortex ring and thus contributes to the deformation of the ring core. The deflection of vortex lines from the main vortex ring persists during the whole motion and is responsible for the gradual erosion of the coherent toroidal structure of the initial vortex ring.